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Quantifying hydrogen uptake by porous materials

MH 2014 Summer School Salford, 17th July 2014

Nuno Bimbo

Postdoctoral Research Officer Department of Chemical Engineering University of Bath N.M.M.Bimbo@bath.ac.uk http://www.bath.ac.uk/chem-eng/people/bimbo

• Hydrogen storage in porous materials
• Experimental measurements
• Absolute and excess adsorption
• Critical points in supercritical adsorption
• Quantifying hydrogen in porous systems
• A model for supercritical gas adsorption
• Fitting experimental data to the model
• Parameters – adsorbed density, pore volume
• Hydrogen densities
• Constant density of adsorbate
• Adsorptive hydrogen storage
• Compression vs adsorption
• Optimal conditions for adsorptive storage
• Adsorbed hydrogen as an energy store
• Thermodynamics of adsorption
• The isosteric enthalpies of adsorption
• Clapeyron and Clausius-Clapeyron
• The virial equation

Outline

Motivation

Food 60 % increase by 2050 (in comparison with 2005/7) Water 55 % increase 2050 Energy 40 % increase by 2035 The energy, food and water nexus Sustainability of elements

UN FAO - World Agriculture towards 2030/2050 (2012) UN Water - World Water Development Report (2014) IEA - World Energy Outlook 2011 tce, October 2011 issue, IChemE

Hydrogen storage

Liquefaction (at 20 K and 1 bar) Compression (at 298 K and 350

• r 700 bar)

Alternative ways of storage include:

Metal hydrides Chemical hydrides

David, WIF. Faraday Discuss (2011) 151, 399-414 (adapted from DOE 2011 Annual Merit Review – Storage)

Cryogenic adsorption Sodium alanate AX-21 Ammonia borane

Hydrogen storage

Eberle et al. Angewandte Chemie International Edition (2009) 48, 6608-6630

• Storage in porous materials can increase its volumetric density at higher

temperatures than liquefaction and lower pressures than compression

• Synthetic chemistry of highly porous materials has known tremendous

developments and new materials include metal-organic frameworks and porous polymers

Furukawa, Yaghi et al. Science (2010), 329, 5990 Farha, Hupp et al. Nat Chem (2010), 2, 944 Yuan, Zhou et al. Adv Mat (2011), 23, 3723 ISI Web of Knowledge

MOF-210 (6,240 m2 g-1) NU-100 (6,100 m2 g-1) PPN-4 (6,400 m2 g-1)

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2000 4000 6000 8000 10000 12000 14000 16000

Topic: metal-organic frameworks

Hydrogen storage in porous materials

Hydrogen storage in porous materials

Experimental measurements High-pressure adsorption in a porous material

Hiden IGA – 2 MPa range (gravimetric) Micromeritics ASAP 2020 – 0.1 MPa range (volumetric) Hiden HTP-1 – 20 MPa range (volumetric) MAST TE7 Carbon beads H2 isotherms in the 86 to 200 K range, up to 14 MPa

2 4 6 8 10 12 14 0.0 0.5 1.0 1.5 2.0 2.5

H2 excess gravimetric uptake / wt.% absolute pressure P / MPa 86.53 K 100.78 K 120.16 K 150.14 K 200.16 K

Hydrogen storage in porous materials

Absolute and excess adsorption

Because adsorptive storage of hydrogen will most likely occur above the critical temperature and at high pressures, understanding and quantifying absolute adsorption is critical Experimental sorption techniques (volumetric and gravimetric) can only account for excess adsorption In a supercritical fluid, this difference is negligible at low pressures but becomes very significant with increasing pressures

Hydrogen storage in porous materials

Critical points in supercritical adsorption Critical points in high-pressure, supercritical adsorption

Excess reaches a maximum and then starts to decrease with increasing density in the bulk, until eventually reaching zero

 

a b e a b e a

V n n n n n     

max max max

, , ,

e e e a

P P n n

 

e

P P a b 

  

Absolute quantity is the excess quantity plus the bulk quantity in the potential field of the adsorbent When the excess reaches a maximum, the gradient of the absolute adsorbed quantity is equal to the gradient of the bulk quantity

T b T a

P n P n                 

when

max e

P P 

Bimbo et al. Faraday Discussions (2011) 151, 59

Leachman et al. J Phys Chem Ref Data (2009) 38

Hydrogen storage in porous materials

Ideal vs real gas

• Data for real gas equation taken from NIST database
• Based on Leachman’s Equation of state for normal hydrogen

Hydrogen storage in porous materials

Ideal vs real gas

• Leachman’s EOS is a complex equation
• A rational fit at different temperatures is done to obtain the densities at different pressures

 

RT P Z T P

H

1 ,

2

 

2 4 3 2 2 1

1 1 ) ( P A P A P A P A P Z     

Quantifying hydrogen in porous materials

A model for supercritical gas adsorption

b n a n e n  

 max a n

a

n 

Absolute Amount in bulk

p V b

b

n





RT P P A P A P A P A RT P Z

b 2 4 3 2 2 1

1 1 1 1       

Density

p V b a n e n     max

p

V RT P Z a n e n 1 max   

Quantifying hydrogen in porous materials

A model for supercritical adsorption

Myers and Monson. Langmuir (2002) 18, 10261; Leachman et al. J. Phys. Chem. Ref. Data (2009) 38, 721; Langmuir. J Am Chem Soc (1918) 40, 1361; Sips. J Chem Phys (1948) 16, 490; Tóth, Acta Chim Acad Sci Hung (1962) 32, 39; Honig and Reyerson, J Phys Chem (1952) 56, 140; Quiñones and Guiochon, J Colloid Interface Sci (1996) 183, 57; Dubinin and Astakhov, Izv Akad Nauk SSSR, Ser Khim (1971), 5, 11; Dubinin and Astakhov, Russ Chem Bull (1971) 20, 8; Bimbo et al. Faraday Discuss (2011) 151, 59

IUPAC Type I equations (θ) Each has different parameters Langmuir (1) Tóth (2) Sips (4) UNILAN (5) Jovanović-Freundlich (3) Dubinin-Astakhov (6) Dubinin-Radushkevich (7)

 max a n a n 

Determined from fitting

bP bP   1 

 

c c bP bP 1 1

      

 

(1) (2)

c bP e ) ( 1    

   c

bP c bP   1 

(4) (3)

           

    ) exp( 1 ) exp( 1 ln 2 1 c bP c bP c 

(5)

m P P m T E E RT e

               

  ln   

(6) (7)

2 ln 2

               

  P P T E E RT e   

Quantifying hydrogen in porous materials

A model for supercritical adsorption

Hydrogen Isotherm for MAST TE-7 carbon beads at 86 K Excess fitted with the Tóth equation Hydrogen Isotherms for MAST TE-7 carbon beads at 86 K Excess and absolute using the Tóth equation

Non-linear fitting

2 4 6 8 10 12 14 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

H2 excess gravimetric uptake / wt.% absolute pressure P / MPa

2 4 6 8 10 12 14 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

H2 excess gravimetric uptake / wt.% absolute pressure P / MPa

a e

V RT P Z n n

a

1

max 

  

max

a

n na 

Experimental points (dependent and independent variable, respectively) Variable parameters (determined from the fitting)

a e

V n P n

a

, ,

max

Quantifying hydrogen in porous materials

Fitting experimental data to the model

Metal-organic framework MIL-101 Activated carbon TE7 Activated carbon AX-21

Materials BET Surface area (m2

g-1)

Skeletal density (g cm-3) Micropore volume (cm3

g-1)

MAST TE7 carbon beads 810 1.94 0.43 AX-21 2258 2.23 1.03* MIL-101 2886 1.69 1.51**

*Quirke and Tennison, Carbon (1996), 34, 1281-1286 **Streppel and Hirscher. Phys Chem Chem Phys (2011) 13, 3220-3222

Quantifying hydrogen in porous materials

Fitting experimental data to the model

TE7 fitted with the Sips equation TE7 fitted with the Dubinin-Radushkevich equation TE7 fitted with the Jovanović-Freundlich equation TE7 fitted with the Tóth equation TE7 fitted with the UNILAN equation TE7 fitted with the Dubinin-Astakhov equation

Quantifying hydrogen in porous materials

Parameters – TE7

Quantifying hydrogen in porous materials

Parameters – AX-21

Quantifying hydrogen in porous materials

Parameters – MIL-101

Quantifying hydrogen in porous materials

Fitting experimental data to the model

MAST TE7 carbon beads – extrapolation to higher pressures using the parameters from the multi-fit of different Type I isotherms at 100 K

10 20 30 40 2.0 2.5 3.0 3.5 4.0

H2 excess gravimetric uptake / wt.% absolute pressure P / MPa Tóth Sips Langmuir Jovanovic-Freundlich UNILAN Dubinin-Radushkevich Dubinin-Astakhov

Quantifying hydrogen in porous materials

Verifying the model - NMR

Anderson et al. J Am Chem Soc (2010) 132, 8618

2 4 6 8 10 1 2 3 4 5 6

gravimetric uptake / wt.% absolute pressure P / MPa CO2-9-1 - 542 m

2 g

• 1

CO2-9-26 - 1027 m

2 g

• 1

CO2-9-59 - 1986 m

2 g

• 1

CO2-9-80 - 3103 m

2 g

• 1

Steam-9-20 - 1294 m

2 g

• 1

Steam-9-35 - 981 m

2 g

• 1

Steam-9-70 - 1956 m

2 g

• 1

PEEK Carbons at 100 K

Quantifying hydrogen in porous materials

Verifying the model - NMR

PEEK Carbon Steam-9-35 HTP volumetric excess, NMR absolute estimation and absolute uptake from modelling PEEK Carbon Steam-9-20 HTP volumetric excess, NMR absolute estimation and absolute uptake from modelling

2 4 6 8 10 12 14 16 18 20 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

H2 uptake / wt.% absolute pressure P / MPa Excess data Fitted excess with the Tóth Absolute estimation with the Tóth Absolute uptake with the NMR

2 4 6 8 10 12 14 16 18 20 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

H2 uptake / wt.% absolute pressure P / MPa Excess data Fitted excess with the Tóth Absolute estimation with the Tóth Absolute uptake with NMR

Quantifying hydrogen in porous materials

Parameters – densities and maximum capacities

From fitting

* max * A a LIM A

n   

From experiment

A a LIM A

n  

max



Using the Tóth equation

Quantifying hydrogen in porous materials

Density of hydrogen

V-L Critical point Triple point

T, P 33.145 K 1.296 MPa 13.957 K 0.007 MPa ρ (kg m-3) Liquid 31.26 77.01

Leachman et al. J Phys Chem Ref Data (2009) 38

Quantifying hydrogen in porous materials

Density of hydrogen

A compressible liquid And a compressible solid…

Johnston et al. J Am Chem Soc (1954) 76, 1482 Silvera, Rev Mod Phys (1980), 52, 393

Para-hydrogen at 4 K 20.38 K

Quantifying hydrogen in porous materials

Density of adsorbed hydrogen

Solid density at 4 K and 0 MPa Liquid density at the triple point Liquid density at the V-L critical point

Quantifying hydrogen in porous materials

Constant density of adsorbate

Excess adsorption + Absolute adsorption + Total adsorption

 

P A B A E

V m     

Sharpe et al. Adsorption (2013), 19, 643 Bimbo et al. Adsorption (2014), 20, 373

Excess adsorption

P A b E A P A A A

V m m V m        

Absolute adsorption

 

P B E T A P B P A A T

V m m V V m            1

Total adsorption

Quantifying hydrogen in porous materials

Constant density of adsorbate

Bimbo et al. Adsorption (2014), 20, 373 Ting et al. Submitted

AX-21 fitted at 90 K TE7 fitted with the Tóth

Quantifying hydrogen in porous materials

Constant density of adsorbate

Ting et al. Submitted

TE7 fitted with the Tóth

2 4 6 8 10 0.0 0.5 1.0 1.5 2.0 2.5

1E-3 0.01 0.1 1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

H2 uptake / wt.% Absolute pressure, P / MPa

Modelled absolute INS integrated elastic line

INS on TE7

Adsorptive hydrogen storage

Compression vs Adsorption

Comparing quantity adsorbed with the quantity at the same P and T without an adsorbent

2 4 6 8 10 12 14 16 18 20 22 24 10 20 30 40 50

g H2 L

• 1

absolute pressure P / MPa

100 .%, ,

2  Solid H a

m m wt n

Calculate mass of solid in 1 L using density of solid ρs (from He pycnometry)

77 K 100 K 120 K 150 K 180 K 200 K Compression at the same temperature

TE7

Bimbo et al. Colloids and Surfaces A (2013), 437, 113

Adsorptive hydrogen storage

Compression vs Adsorption

77 K 100 K 120 K 150 K 180 K 200 K Compression at the same temperature

MIL-101

2 4 6 8 10 12 14 16 18 20 22 24 10 20 30 40 50

g H2 L

• 1

absolute pressure P / MPa

2 4 6 8 10 12 14 16 18 20 22 24 10 20 30 40 50

g H2 L

• 1

absolute pressure P / MPa

Bimbo et al. Colloids and Surfaces A (2013), 437, 113

AX-21

60 80 100 120 140 160 180 200 2 4 6 8 10 12 14 16 18 20

Absolute pressure, P / MPa Temperature, T / K

AX-21 MIL-101 MAST TE7 carbon beads

Adsorptive hydrogen storage

Compression vs Adsorption

Bimbo et al. Colloids and Surfaces A (2013), 437, 113

MAST TE7 Carbon beads at 100 K Comparison with compression MIL-101 at 100 K Comparison with compression AX-21 at 100 K Comparison with compression

2 4 6 8 10 12 14 16 18 20 22 24 5 10 15 20 25 30 35 40 45

g H2 L

• 1

absolute pressure P / MPa Full of adsorbent (1056 g) Filling ratio 0.75 Filling ratio 0.50 Filling ratio 0.25 No adsorbent

2 4 6 8 10 12 14 16 18 20 22 24 5 10 15 20 25 30 35 40 45

g H2 L

• 1

absolute pressure P / MPa Full of adsorbent (475 g) Filling ratio 0.75 Filling ratio 0.5 Filling ratio 0.25 No adsorbent

2 4 6 8 10 12 14 16 18 20 22 24 5 10 15 20 25 30 35 40 45

g H2 L

• 1

absolute pressure P / MPa Full of adsorbent (676 g) Filling ratio 0.75 Filling ratio 0.5 Filling ratio 0.25 No adsorbent

t c

V V 

Filling ratio

   

c t b a

V V mass n n     

a sk c a c t

V mass V V V V     

Adsorptive hydrogen storage

Optimal conditions of storage

Bimbo et al. Colloids and Surfaces A (2013), 437, 113

MAST TE7 Carbon beads at 100 K AX-21 at 100 K

2 4 6 8 10 12 14 16 18 20 22 24 5 10 15 20 25

g H2 L

• 1

absolute pressure P / MPa Full of adsorbent (676 g) Filling ratio 0.75 Filling ratio 0.5 Filling ratio 0.25

2 4 6 8 10 12 14 16 18 20 22 24 5 10 15 20 25

g H2 L

• 1

absolute pressure P / MPa Full of adsorbent (475 g) Filling ratio 0.75 Filling ratio 0.5 Filling ratio 0.25

2 4 6 8 10 12 14 16 18 20 22 24 5 10 15 20 25

g H2 L

• 1

absolute pressure P / MPa Full of adsorbent (1056 g) Filling ratio 0.75 Filling ratio 0.5 Filling ratio 0.25

MIL-101 at 100 K

Adsorptive hydrogen storage

Comparison – energy stored

Sharpe et al. Microporous and Mesoporous Materials, COPS-X Special Edition (submitted)

VC

– Container volume

VB

– Bulk hydrogen volume

VD

– Displaced volume

VT

– Total adsorbate volume

VF

– Volume of tank containing adsorbent

VBI

– Volume of bulk hydrogen in the interstitial sites

VBC

– Volume of bulk hydrogen in the tank containing no adsorbent

VBP

– Volume of bulk hydrogen in the pores of the adsorbent

VS

– Skeletal volume of the adsorbent

VP

– Open pore volume

VA

– Adsorbate volume

f – fill factor x – packing factor of adsorbent

Adsorptive hydrogen storage

Comparison – energy stored

Sharpe et al. Microporous and Mesoporous Materials, COPS-X Special Edition (submitted)

Adsorptive hydrogen storage

Comparison – energy stored

Sharpe et al. Microporous and Mesoporous Materials, COPS-X Special Edition (submitted)

90 K 100 K

Adsorptive hydrogen storage

Comparison – energy stored

Sharpe et al. Microporous and Mesoporous Materials, COPS-X Special Edition (submitted)

77 K 90 K

Adsorptive hydrogen storage

Comparison – energy stored

Sharpe et al. Microporous and Mesoporous Materials, COPS-X Special Edition (submitted)

77 K 90 K

Adsorptive hydrogen storage

Comparison – energy stored

Sharpe et al. Microporous and Mesoporous Materials, COPS-X Special Edition (submitted)

TE7 Carbon beads at 89 K

Adsorptive hydrogen storage

Comparison – energy stored

Sharpe et al. Microporous and Mesoporous Materials, COPS-X Special Edition (submitted)

Bimbo et al. Faraday Discuss (2011) 151, 59 Bimbo et al. Adsorption (2014), 20, 373-384

Thermodynamics of adsorption

Isosteric enthalpies of adsorption

v S T P

A

n

          

Clapeyron equation (exact)

ab ab n

v T h T P

A

          

Assume:

• Ideal gas
• Negligible molar volume for the adsorbate
• Enthalpy of adsorption is independent of temperature

(Heat capacity of the adsorbed phase is zero)

a a b ab

v v v v      P RT va    P RT vab   

Enthalpies of adsorption

• Measure of the heat released upon adsorption
• Should be calculated over absolute adsorption, not excess

Isosteric method

• Pressure at constant amount adsorbed

Bimbo et al. Faraday Discuss (2011) 151, 59 Bimbo et al. Adsorption (2014), 20, 373-384

Thermodynamics of adsorption

Clapeyron and Clausius-Clapeyron

v T h T P

A

n

          

2

RT h P P RT T h T P

ab ab nA

              R h T P

ab nA

                 1 ln

Integrating Clausius-Clapeyron equation

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

• 12
• 10
• 8
• 6
• 4
• 2

2 4

ln P / MPa 1000/RT / mol kJ

• 1

Loading / wt.% 0.1 0.5 1 2 4 6 7

Isosteres for hydrogen adsorption in Cu2(tptc) (NOTT-101) fitted with the Clausius-Clapeyron approximation, 50-87 K range, up to 4 MPa

Bimbo et al. Faraday Discuss (2011) 151, 59 Bimbo et al. Adsorption (2014), 20, 373-384

Thermodynamics of adsorption

Clapeyron and Clausius-Clapeyron

ab ab n

v T h T P

A

          

But we can calculate exact molar volumes from the model and solve the differential numerically

NOTT-101

MIL-101 AX-21

Czepirski and Jagiello, Chem Eng Sci (1989), 44, 797

Thermodynamics of adsorption

Virial equation

 

 

       

m j j j l j j j

n b n a T n P 1 ln

Both with m and l = 5





 

l j j j st

n a R Q

• 1

1 2 3 4 5 6 7 1 2 3 4 5 6 7

Clausius-Clapeyron Clapeyron equation virial equation (m=5, l=4) virial equation (m=5, l=5) Isosteric enthalpy, Qst / kJ mol

• 1

Absolute uptake / wt. %

MIL-101 AX-21

• 1

1 2 3 4 5 6 1 2 3 4 5 6 7 8 9

Clausius-Clapeyron equation Clapeyron equation virial equation (m=5, l=4) virial equation (m=5, l=5) Isosteric enthalpy, Qst / kJ mol

• 1

Absolute uptake / wt. %

Bimbo et al. Adsorption (2014), 20, 373-384

Thermodynamics of adsorption

The virial equation Clapeyron, Clausius-Clapeyron and virial

Methane adsorption Hydrogen kinetics

Other work

2 4 6 8 10 12 14 16 80 90 100 110 120 130 140 150

Data Fitted LDF

Amount adsorbed, n /  moles time, t / minutes

Kinetic curve for Hydrogen on AX-21 (90 K, Pf = 2.517 kPa)

2 4 6 8 10 12 14 16 18 2 4 6 8 10 12

CH4 gravimetric uptake

• wt. %

Absolute Pressure, P / MPa 210 K 230 K 250 K 273.15 K 300 K 325 K 350 K

Methane adsorption on HKUST-1

Acknowledgements

Tim Mays Research Group (http://people.bath.ac.uk/cestjm) Valeska Ting and Andrew Physick (http://people.bath.ac.uk/vt233) Funding and Facilites

Acknowledgements

Thank you!